Question

2+4+6+8+.......+2000=?
Suma lui gauss

Answer 1

Dam factor comun pe 2, astfel S= 2(1+2+3+.....+1000)
1+2+3+...+1000= 1000X1001/2 = 1.001.000/2= 500.500
S= 2X500500
S=1001000

Answer 2

$\displaystyle 2+4+6+8+...+2000=2(1+2+3+...+1000)= \\ \\ =2 \times \frac{1000(1000+1)}{2} =2 \times \frac{1000 \times 1001}{2} =2 \times \frac{1001000}{2} = \\ \\ = 2 \times 500500=1001000$